What do we call a segment whose endpoints lie on a circle?

A segment whose endpoints lie on a circle is called a chord. The definition of a chord is specifically tied to its endpoints being on the circumference of the circle. It spans the interior of the circle and is entirely contained within it.

In contrast, a diameter is a special type of chord that passes through the center of the circle and is the longest possible chord in a circle. A radius is defined as the distance from the center of the circle to any point on its circumference and is not a segment that connects two points on the circumference, but rather spans from the center to the edge. An arc, on the other hand, refers to a portion of the circumference of the circle and is not defined as a straight line segment.

Thus, a chord is the term that specifically describes a segment connecting two points on the circle’s edge, making it the correct choice.